Step-by-step explanation:

x2 - 4x - 12

Simplify ————————————

x2 - 2x - 24

The first term is, x2 its coefficient is 1 .

The middle term is, -4x its coefficient is -4 .

The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

-12 + 1 = -11

-6 + 2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2

x2 - 6x + 2x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-6)

Add up the last 2 terms, pulling out common factors :

2 • (x-6)

Step-5 : Add up the four terms of step 4 :

(x+2) • (x-6)

Which is the desired factorization

Factoring x2-2x-24

The first term is, x2 its coefficient is 1 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -24

Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24

Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -2 .

-24 + 1 = -23

-12 + 2 = -10

-8 + 3 = -5

-6 + 4 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 4

x2 - 6x + 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-6)

Add up the last 2 terms, pulling out common factors :

4 • (x-6)

Step-5 : Add up the four terms of step 4 :

(x+4) • (x-6)

Which is the desired factorization

Cancel out (x-6) which appears on both sides of the fraction line.

Final result :

x + 2

—————

x + 4